Although brukar can carry that meaning, it is today most often used for meaning habitually, regularly rather than usually. Thus the use here means that it's a recurring phenomenon, and that it happens often.

No, that's another accepted answer.

That would mean that he puts the clothes on.

Yeah, I'm wondering that too, especially as there's another similar sentence which just uses oftast like that without brukar... 'Oftast lagar vi mat själva'. Why is it not ok this time?

'Brukar' is the conjugated verb here (unlike English 'usually'), so 'ha' is in the infinitive form (much as it is in 'vill ha', etc.). I think an overly-literal rendering would be something like 'he makes use most often to have green clothes on himself'.